What is the general solution for 2tan(θ)-sec(θ)=0 ?

The general solution for 2tan(θ)-sec(θ)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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2tan(θ)-sec(θ)=0

2 tan (θ) - sec (θ) = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

2 tan (θ) - sec (θ) = 0

Express with sin, cos

\frac{- 1 + 2 sin ( θ )}{cos ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- 1 + 2 sin (θ) = 0

Move

1

to the right side

2 sin (θ) = 1

Divide both sides by

2

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = \frac{175}{214}

2 \cdot cos^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq π

2 cos^{3} (x) - cos^{2} (x) = 0

sin^{2} (x) - 2 = sin (x)

arccosh (x) = \frac{2 π}{7}

What is the general solution for 2tan(θ)-sec(θ)=0 ?
The general solution for 2tan(θ)-sec(θ)=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin